Matosas, 51, will officially take charge in January as Los Ticos prepare for the start of their 2022 World Cup qualifying campaign, the Costa Rican football federation said, reports Xinhua news agency.
"It's a wonderful challenge that I am very excited about," Matosas told a news conference on Tuesday.
"I will treat the opportunity as if it were my own country's national team."
Costa Rica is currently led by Ronald Gonzalez, who replaced Oscar Ramirez on an interim basis following the team's disappointing results in the 2018 World Cup in Russia.
Matosas, a former midfielder who was capped seven times for Uruguay's national team, has coached at 14 different clubs since retiring as a player in 2001. Costa Rica will be his first experience as a manager at the international level.
(With inputs from agencies.)